Mr DE morgan, ON THE BEATS OF IMPERFECT CONSONANCES. 



131 



Here we have intervals of -54 and -39, altogether '93, of a mean semitone. Mr Woolhouse's 

 experiment gives 254 double vibrations to the C immediately below; and other experiments 

 give nearly the same, for our day. The common tradition is that concert-pitch has risen 

 about a note in the last century. The change can be traced in its progress. Robison, at 

 the end of the last century, found the ordinary tuning-forks gave 240 vibrations for C, that is, 

 270 vibrations for D, a little higher than Dr Smith's organ at its warmest. Possibly some of 

 this effect may have arisen as follows. The organs being tuned in the cold to the usual pitch 

 of the day, the orchestras, on tuning with them after the air had been warmed by a crowd, 

 would find it necessary to raise their pitch. This would have a tendency to cause a perma- 

 nent rise, which the organ-tuners would of course follow, and then the same effect would be 

 repeated. The convenience of representing the Cs by powers of 2 has led many writers to 

 choose 256 as the number of double vibrations in the first C below the lines of the treble: I 

 trust this power of 2 will be enough to prevent the pitch from making any further ascent. 



The subject to which I now come has been perplexed from the beginning by a confusion 

 of different things under one word. By a beat, I mean any acoustical cycle derived from 

 composition of ordinary vibrations ; whether the returns can be distinguished by the ear as 

 separate occurrences, or whether they are rapid enough to cause a sound. The first kind* of 

 beats were used by Sauveur: but as there is a confused discussion about them in which his 

 name occurs, it will be more convenient to call them Tartini's heats, because, when they 

 become rapid enough to give a note, that note is the grave harmonic detected by Tartini in or 



Hon; they make it difficult to know whether they mean the 

 single wave, be it of condensation or of rarefaction, or the 

 double wave made up of one condensation and one rarefaction. 

 Much confusion might have been saved in many subjects if 

 terms of contempt, or of slang, had been seriously adopted : 

 for such terms are very often more expressive than the solemn 

 words which they are directed at. The " previous examina- 

 tion" is very feeble compared with the "little-go." For the 

 present case, when the pendulum was brought into use, it was 

 called in derision a swing-swang. If this word had been 

 adopted by writers on acoustics, all the confusion I speak of 

 would have been prevented; for no writer would have left it in 

 doubt whether he reckoned in swings, or in swing-swangs, as 

 I shall do. There is the same difficulty in medical descrip- 

 tions, occasionally : some have counted inspiration and respira- 

 tion as one, most as two. 



• The organ tuners must in all time have known the beats 

 which disappear when the concord becomes perfect. The first 

 writer who is cited as having mentioned them is Mersenne 

 ( Harmonie Universelle, Paris, 1636, folio, book on instruments, 

 p. 362). But Mersenne does not attempt any explanation. He 

 observes that two pipes which are nearly unisons tremble, 

 and make the hand which holds them tremble. But the trem- 

 bling goes off when the unison is made perfect ; which, says 

 Mersenne, is the exact opposite of what takes place in strings. 

 That is, he imagined the beats were to be compared with the 

 sympathetic vibrations. Dr Smith, with that habit of indis- 

 tinctive citation which is one of the manias of much learning, 

 cites Mersenne and Sauveur together as his predecessors in 

 the subject. 



There is another writer who is better qualified to be classed 



as the immediate predecessor of Sauveur, because he distinctly 

 opposes the sympathy of consonant vibrations, and its effects, to 

 the clashing of dissonant vibrations. I mean Dr Wm. Holder, 

 r.R.S., who died in January 1696-7, and was the opponent of 

 Wallis on a question of priority in the method of teaching 

 the deaf and dumb. In his Natural Grounds and Principles of 

 Harmony, published in 1694, he describes beats in a manner 

 which is worth quoting, were it only as an instance of the 

 poetry of explanation which science has driven out (pp. 34, 35, 

 ed. of 1731):— 



" It hath been a common Practice to imitate a Tabour and 

 Pipe upon an Organ. Sound together two discording Keys 

 (the base Keys will shew it best, because their Vibrations are 

 slower), let them, for Example, be Gamut with Gamut sharp, 

 or F Faut sharp, or all three together. Though these of them- 

 selves should be exceeding smooth and well voyced Pipes, yet, 

 when struck together, there will be such a Battel in the Air 

 between their disprbportioned Motions, such a Clatter and 

 Thumping, that it will be like the beating of a Drum, while a 

 Jigg is played to it with the other hand. If you cease this, and 

 sound a full Close of Concords, it will appear surprizingly 



smooth and sweet Being in an Arched sounding Room 



near a shrill Bell of a House Clock, when the Alarm struck, 

 I whistled to it, which I did with ease in the same Tune with 

 the Bell, but, endeavouring to whistle a Note higher or lower, 

 the Sound of the Bell and its cross Motions were so predomi- 

 nant, that my Breath and Lips were check'd, that I could not 

 whistle at all, nor make any sound of it in that discording 

 Tune. After, I sounded a shrill whistling Pipe, which was 

 out of Tune to the Bell, and their Motions so clashed, that 

 they seemed to sound like switching one another in the Air." 



17—2 



